Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice

Abstract

We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with "expanded" vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {\pm}4,{\pm}3,{\pm}2 and {\pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.

arXiv comment9 pages, 9 figures

References in corpus (40)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Kitaev-Heisenberg Model on Honeycomb Lattice: Possible Exotic Phases in Iridium Oxides $A_2$IrO${}_3$
• Exact results for spin dynamics and fractionization in the Kitaev Model
• An exact chiral spin liquid with non-Abelian anyons
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Exactly solvable Kitaev model in three dimensions
• Zoology of Fractional Chern Insulators
• Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Topological insulators and fractional quantum Hall effect on the ruby lattice
• Disorder in a quantum spin liquid: flux binding and local moment formation
• Algebraic spin liquid in an exactly solvable spin model
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Bond Algebras and Exact Solvability of Hamiltonians: Spin S=1/2 Multilayer Systems and Other Curiosities
• Topological states and braiding statistics using quantum circuits
• Mosaic spin models with topological order
• A $\Gamma$-matrix generalization of the Kitaev model
• Perturbative approach to an exactly solved problem: the Kitaev honeycomb model
• Optical Kagome lattice for ultra-cold atoms with nearest neighbor interactions
• Three-dimensional topological phase on the diamond lattice
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Magnetic impurities in the honeycomb Kitaev model
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Quantum spin metal state on a decorated honeycomb lattice
• Interacting Anyonic Fermions in a Two-Body Color Code Model
• Topological Insulators and Quantum Spin Liquids
• Nature of a topological quantum phase transition in a chiral spin liquid model
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Exact results for the star lattice chiral spin liquid
• Exactly Solvable Topological Chiral Spin Liquid with Random Exchange
• Exact quantum spin liquids with Fermi surfaces in spin-half models
• Gauge symmetry in Kitaev-type spin models and index theorems on odd manifolds

Cited by in corpus (5)

• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Kitaev spin models from topological nanowire networks
• Dynamics of a two-dimensional quantum spin-orbital liquid: spectroscopic signatures of fermionic magnons
• Exactly Solvable 1D Quantum Models with Gamma Matrices
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice